Question

A project manager estimates that a project will take x hours to complete, where x > 100. The goal is for the estimate to be within 10 hours of the time it will actually take to complete the project. If the manager meets the goal and it takes y hours to complete the project, which of the following inequalities represents the relationship between the estimated time and the actual completion time?

• A. $x+y<10$
• B. $y>x+10$
• C. $x-10$
• D. $-10<y-x<10$

Answer 1

The correct option is D $-10<y-x<10$

The estimated completion time for the project is denoted by x and the actual completion time is denoted by y. The requirement is that the actual time is within 10 hours of the estimate. Therefore, the requirement is that the difference in actual and estimated completion times (the absolute value) is less than 10 hours. Therefore,
$|y-x|\le 10\Rightarrow -10<y-x<10$